Problem: Simplify the following expression: $\dfrac{60q^3}{20q^4}$ You can assume $q \neq 0$.
Solution: $ \dfrac{60q^3}{20q^4} = \dfrac{60}{20} \cdot \dfrac{q^3}{q^4} $ To simplify $\frac{60}{20}$ , find the greatest common factor (GCD) of $60$ and $20$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $20 = 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(60, 20) = 2 \cdot 2 \cdot 5 = 20 $ $ \dfrac{60}{20} \cdot \dfrac{q^3}{q^4} = \dfrac{20 \cdot 3}{20 \cdot 1} \cdot \dfrac{q^3}{q^4} $ $\phantom{ \dfrac{60}{20} \cdot \dfrac{3}{4}} = 3 \cdot \dfrac{q^3}{q^4} $ $ \dfrac{q^3}{q^4} = \dfrac{q \cdot q \cdot q}{q \cdot q \cdot q \cdot q} = \dfrac{1}{q} $ $ 3 \cdot \dfrac{1}{q} = \dfrac{3}{q} $